10
43
(K10a
52
)
A knot diagram
1
Linearized knot diagam
5 1 9 7 2 10 4 3 8 6
Solving Sequence
3,9
4 8 10 7 5 6 1 2
c
3
c
8
c
9
c
7
c
4
c
6
c
10
c
2
c
1
, c
5
Ideals for irreducible components
2
of X
par
I
u
1
= hu
36
− u
35
+ ··· − u
2
+ 1i
* 1 irreducible components of dim
C
= 0, with total 36 representations.
1
The image of knot diagram is generated by the software “Draw programme” developed by An-
drew Bartholomew(http://www.layer8.co.uk/maths/draw/index.htm#Running-draw), where we modi-
fied some parts for our purpose(https://github.com/CATsTAILs/LinksPainter).
2
All coefficients of polynomials are rational numbers. But the coefficients are sometimes approximated
in decimal forms when there is not enough margin.
1
I. I
u
1
= hu
36
− u
35
+ · · · − u
2
+ 1i
(i) Arc colorings
a
3
=
1
0
a
9
=
0
u
a
4
=
1
−u
2
a
8
=
−u
u
a
10
=
u
3
−u
3
+ u
a
7
=
−u
3
u
5
− u
3
+ u
a
5
=
u
6
− u
4
+ 1
−u
8
+ 2u
6
− 2u
4
a
6
=
−u
11
+ 2u
9
− 2u
7
− u
3
u
11
− 3u
9
+ 4u
7
− u
5
− u
3
+ u
a
1
=
u
19
− 4u
17
+ 8u
15
− 8u
13
+ 5u
11
− 2u
9
+ 2u
7
+ u
3
−u
19
+ 5u
17
− 12u
15
+ 15u
13
− 9u
11
− u
9
+ 4u
7
− 2u
5
− u
3
+ u
a
2
=
−u
33
+ 8u
31
+ ··· + 2u
3
− u
u
35
− 9u
33
+ ··· − u
3
+ u
(ii) Obstruction class = −1
(iii) Cusp Shapes
= −4u
35
+40u
33
−4u
32
−192u
31
+36u
30
+564u
29
−156u
28
−1092u
27
+412u
26
+1380u
25
−
712u
24
−980u
23
+ 792u
22
+ 16u
21
−480u
20
+ 732u
19
−16u
18
−680u
17
+ 280u
16
+ 112u
15
−
188u
14
+ 272u
13
−12u
12
−216u
11
+ 80u
10
−36u
8
+ 80u
7
−8u
6
−32u
5
+ 8u
4
−4u
3
+ 8u + 2
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
5
u
36
+ u
35
+ ··· − u
2
+ 1
c
2
u
36
+ 19u
35
+ ··· + 2u + 1
c
3
, c
8
u
36
− u
35
+ ··· − u
2
+ 1
c
4
, c
7
u
36
− 3u
35
+ ··· − 22u + 5
c
6
, c
10
u
36
+ 3u
35
+ ··· + 22u + 5
c
9
u
36
− 19u
35
+ ··· − 2u + 1
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
8
y
36
− 19y
35
+ ··· − 2y + 1
c
2
, c
9
y
36
− 3y
35
+ ··· + 2y + 1
c
4
, c
6
, c
7
c
10
y
36
+ 25y
35
+ ··· − 154y + 25
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.805609 + 0.585926I
−5.78512 + 6.60899I −5.22618 − 6.99003I
u = 0.805609 − 0.585926I
−5.78512 − 6.60899I −5.22618 + 6.99003I
u = −0.973666 + 0.342560I
− 3.75301I 0. + 6.73664I
u = −0.973666 − 0.342560I
3.75301I 0. − 6.73664I
u = −0.771553 + 0.550437I
−2.48653 − 2.21040I −2.18679 + 3.72055I
u = −0.771553 − 0.550437I
−2.48653 + 2.21040I −2.18679 − 3.72055I
u = 0.733643 + 0.592284I
−5.99129 − 1.96554I −6.00564 + 0.22737I
u = 0.733643 − 0.592284I
−5.99129 + 1.96554I −6.00564 − 0.22737I
u = 0.879174 + 0.103222I
1.48890 + 0.27307I 6.50261 − 0.38004I
u = 0.879174 − 0.103222I
1.48890 − 0.27307I 6.50261 + 0.38004I
u = −1.079360 + 0.331184I
− 3.70794I 0. + 4.78665I
u = −1.079360 − 0.331184I
3.70794I 0. − 4.78665I
u = 0.193860 + 0.787757I
−2.88545 − 7.72472I −3.24945 + 5.61903I
u = 0.193860 − 0.787757I
−2.88545 + 7.72472I −3.24945 − 5.61903I
u = 1.169940 + 0.367759I
3.90881 + 0.64400I 5.19682 − 0.84878I
u = 1.169940 − 0.367759I
3.90881 − 0.64400I 5.19682 + 0.84878I
u = −0.176866 + 0.751609I
2.99647I 0. − 2.49060I
u = −0.176866 − 0.751609I
− 2.99647I 0. + 2.49060I
u = 0.241156 + 0.725408I
−3.90881 + 0.64400I −5.19682 − 0.84878I
u = 0.241156 − 0.725408I
−3.90881 − 0.64400I −5.19682 + 0.84878I
u = −1.188280 + 0.342283I
1.27958 + 4.07135I 1.88452 − 2.88119I
u = −1.188280 − 0.342283I
1.27958 − 4.07135I 1.88452 + 2.88119I
u = −0.038116 + 0.743633I
2.48653 + 2.21040I 2.18679 − 3.72055I
u = −0.038116 − 0.743633I
2.48653 − 2.21040I 2.18679 + 3.72055I
u = 1.143830 + 0.521070I
−1.27958 + 4.07135I −1.88452 − 2.88119I
u = 1.143830 − 0.521070I
−1.27958 − 4.07135I −1.88452 + 2.88119I
u = 1.184710 + 0.434081I
5.99129 + 1.96554I 6.00564 − 0.22737I
u = 1.184710 − 0.434081I
5.99129 − 1.96554I 6.00564 + 0.22737I
u = −1.184420 + 0.463218I
5.78512 − 6.60899I 5.22618 + 6.99003I
u = −1.184420 − 0.463218I
5.78512 + 6.60899I 5.22618 − 6.99003I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.168380 + 0.513346I
2.88545 − 7.72472I 3.24945 + 5.61903I
u = −1.168380 − 0.513346I
2.88545 + 7.72472I 3.24945 − 5.61903I
u = 1.175040 + 0.526945I
12.6026I 0. − 8.81146I
u = 1.175040 − 0.526945I
− 12.6026I 0. + 8.81146I
u = −0.446315 + 0.412227I
−1.48890 + 0.27307I −6.50261 − 0.38004I
u = −0.446315 − 0.412227I
−1.48890 − 0.27307I −6.50261 + 0.38004I
6
II. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
, c
5
u
36
+ u
35
+ ··· − u
2
+ 1
c
2
u
36
+ 19u
35
+ ··· + 2u + 1
c
3
, c
8
u
36
− u
35
+ ··· − u
2
+ 1
c
4
, c
7
u
36
− 3u
35
+ ··· − 22u + 5
c
6
, c
10
u
36
+ 3u
35
+ ··· + 22u + 5
c
9
u
36
− 19u
35
+ ··· − 2u + 1
7
III. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
, c
3
, c
5
c
8
y
36
− 19y
35
+ ··· − 2y + 1
c
2
, c
9
y
36
− 3y
35
+ ··· + 2y + 1
c
4
, c
6
, c
7
c
10
y
36
+ 25y
35
+ ··· − 154y + 25
8
